| 1. |
- Constantin, Adrian, et al.
(författare)
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Exact periodic traveling water waves with vorticity
- 2002
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Ingår i: Comptes Rendus Mathématique. - 1631-073X. ; 335:10, s. 797-800
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Tidskriftsartikel (refereegranskat)abstract
- For the classical inviscid water wave problem under the influence of gravity, described by the Euler equation with a free surface over a flat bottom, we construct periodic traveling waves with vorticity. They are symmetric waves whose profiles are monotone between each crest and trough. We use global bifurcation theory to construct a connected set of such solutions. This set contains flat waves as well as waves that approach flows with stagnation points.
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| 2. |
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| 3. |
- Gustafsson, Björn, et al.
(författare)
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Explicit limits for nonperiodic homogenization and reduction of dimension
- 2002
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Ingår i: Comptes rendus. Mathematique. - 1631-073X .- 1778-3569. ; 334:11, s. 977-982
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Tidskriftsartikel (refereegranskat)abstract
- The aim of this Note is to give explicit limit expressions. for diffusion equations involving a small parameter E, describing both nonperiodic homogenization and reduction of dimension. We consider two kinds of reduction of dimension: the case of plates and the case of thin cylinders. In particular, we give the limit diffusion equation for stratified plates. This is completely explicit and requires no special assumption, except stratification. In the case of thin cylinders, the formulae are less explicit, but we also indicate some simple applications to fibered materials.
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| 4. |
- Abdulle, Assyr, et al.
(författare)
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Exponential decay of the resonance error in numerical homogenization via parabolic and elliptic cell problems
- 2019
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Ingår i: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 357:6, s. 545-551
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents two new approaches for finding the homogenized coefficients of multiscale elliptic PDEs. Standard approaches for computing the homogenized coefficients suffer from the so-called resonance error, originating from a mismatch between the true and the computational boundary conditions. Our new methods, based on solutions of parabolic and elliptic cell problems, result in an exponential decay of the resonance error.
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| 5. |
- Adiprasito, Karim, et al.
(författare)
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Connectivity of pseudomanifold graphs from an algebraic point of view
- 2015
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Ingår i: Comptes Rendus Mathematiques de l'Academie des Sciences = Mathematical reports of the academy of science. - : Elsevier. - 0706-1994. ; 353:12, s. 1061-1065
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Tidskriftsartikel (refereegranskat)abstract
- The connectivity of graphs of simplicial and polytopal complexes is a classical subject going back at least to Steinitz, and the topic has since been studied by many authors, including Balinski, Barnette, Athanasiadis, and Bjorner. In this note, we provide a unifying approach that allows us to obtain more general results. Moreover, we provide a relation to commutative algebra by relating connectivity problems to graded Betti numbers of the associated Stanley-Reisner rings.
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| 6. |
- Aka, Menny, et al.
(författare)
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On metric Diophantine approximation in matrices and Lie groups
- 2015
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Ingår i: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 353:3, s. 185-189
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Tidskriftsartikel (refereegranskat)abstract
- We study the Diophantine exponent of analytic submanifolds of m x n real matrices, answering questions of Beresnevich, Kleinbock, and Margulis. We identify a family of algebraic obstructions to the extremality of such a submanifold, and give a formula for the exponent when the submanifold is algebraic and defined over Q. We then apply these results to the determination of the Diophantine exponent of rational nilpotent Lie groups.
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| 7. |
- Al Abdulaali, Ahmad, 1981-
(författare)
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The extendability of S-plurisubharmonic currents : = Sur le prolongement des courants S-plurisousharmoniques
- 2012
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Ingår i: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 350:23-24, s. 1023-1026
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- This paper studies the extendability of negative S-plurisubharmonic current of bidimension (p,p) across a (2p-2)-dimensional closed set. Using only the positivity of S, we show that such extensions exist in the case when these obstacles are complete pluripolar, as well as zero sets of C2-plurisubharmoinc functions.
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| 8. |
- Aleman, Alexandru, et al.
(författare)
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Density of disk algebra functions in de Branges–Rovnyak spaces
- 2017
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Ingår i: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 355:8, s. 871-875
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Tidskriftsartikel (refereegranskat)abstract
- We prove that functions analytic in the unit disk and continuous up to the boundary are dense in the de Branges–Rovnyak spaces induced by the extreme points of the unit ball of . Together with previous theorems, it follows that this class of functions is dense in any de Branges–Rovnyak space.
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| 9. |
- Astashkin, Sergey V., et al.
(författare)
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Lp + Lq and Lp ∩ Lq are not isomorphic for all 1 ≤ p,q ≤ ∞, p ≠ q
- 2018
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Ingår i: Comptes rendus. Mathematique. - : Elsevier. - 1631-073X .- 1778-3569. ; 356:6, s. 661-665
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Tidskriftsartikel (refereegranskat)abstract
- We prove that if 1≤p,q≤∞1≤p,q≤∞, then the spaces Lp+LqLp+Lq and Lp∩LqLp∩Lq are isomorphic if and only if p=qp=q. In particular, L2+L∞L2+L∞ and L2∩L∞L2∩L∞ are not isomorphic, which is an answer to a question formulated in [2].
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| 10. |
- Becker, R., et al.
(författare)
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A finite element time relaxation method
- 2011
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Ingår i: Comptes Rendus Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 349:5-6, s. 353-356
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Tidskriftsartikel (refereegranskat)abstract
- We discuss a finite element time-relaxation method for high Reynolds number flows. The method uses local projections on polynomials defined on macroelements of each pair of two elements sharing a face. We prove that this method shares the optimal stability and convergence properties of the continuous interior penalty (CIP) method. We give the formulation both for the scalar convection-diffusion equation and the time-dependent incompressible Euler equations and the associated convergence results. This note finishes with some numerical illustrations. (C) 2010 Academic des sciences. Published by Elsevier Masson SAS. All rights reserved.
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